Changing startup file location
I don't think it is possible to change the path of the startup.blend file, however there are ways you can work around it. As with all things, there is the regular way and then the blender way.

First, the blender way, basically the startup file is not cast in stone. The idea is that you can open any .blend file and save it to startup using Ctrl + U.  So when you next open blender you get a fresh copy of that file.

This might seem like a strange way to do it, but you may spend weeks modelling, then texturing and you may have different needs from your startup file for a given week or month.  So as you mentioned, keep some templates somewhere and just use the hotkey to clone this to your startup.

If you want to do this so you can backup your startup file, you can create a shortcut to your startup.blend and preferences.blend files in a more accessible directory.  On windows you'll find it in your AppData folder (it's hidden by default), this is beyond the scope of this site, but you should be able to locate it with some googling.